This is not true... a motor with higher compression will out perform and engine with less compression every time. All the information that has been added to this thread applies to N/A and Forced Induction engines just the same.
A 13:1 engine and 10lbs. of boost will have much greater cylinder pressure then an engine with 8:1 and 10lbs. of boost.
It's an old rule/idea that you cannot mix high compression with boost... this may have been true for my dads generation but not ours. Not with the advanced electronics we have today! Back in the day everyone was limited by fuel as well as ignition control.
The reason why people lower the compression ratio on a forced induction engine is because of knocking... When the engineers are calibrating the engine, they calibrate something called SBP, that stands for Spark Advance for Best Torque, so the engine is on its knocking limit, and if you install a turbocharger in a factory engine you almost certainly get heavy knocking unless you decrease the compression ratio.
Theorethicaly a higher compression ratio will get you better thermal efficiency, but it is not always the right way to go. Sometimes when you increase the compression ratio, lets say of a NA engine, you can get an engine that does not respond well to spark advance, and that is shit if you want to extract the best performance of the engine.
Also, to explain why the engines performance will improve with higher compression ratio, whe can look at thermodynamics principles. The higher the compression ratio, the hotter the air is at the end of the compression cycle, and that will help you in a number of ways, one of them is the higher vaporitzation of the fuel, and that is one of the main issues on ICE, for combustion will be effective only on gas mixtures, not on liquid gas mixtures, and even with the modern day technology we still dont get 100% fuel vaporization. Another point is, if you have studied thermodynamics you learned that for example in a Rankine cycle thermal efficiency is higher when you preheat the air from combustion, the same applies to ICE. You could ask then why the **** do we use intercoolers? The answer to that has nothing to do with we are talking about, for we are talking about temperatures after compression and on the intercooler case, intake air temperature, which are two different topics